Related papers: Unbalanced Sobolev Descent
An algorithm of searching a zero of an unknown undimensional function is considered, measured at a point x with some error. The step sizes are random positive values and are calculated according to the rule: if two consecutive iterations…
Stochastic gradient descent (SGD), a widely used algorithm in deep-learning neural networks has attracted continuing studies for the theoretical principles behind its success. A recent work reports an anomaly (inverse) relation between the…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
Saddle point problems, ubiquitous in optimization, extend beyond game theory to diverse domains like power networks and reinforcement learning. This paper presents novel approaches to tackle saddle point problem, with a focus on…
Momentum Stochastic Gradient Descent (MSGD) algorithm has been widely applied to many nonconvex optimization problems in machine learning, e.g., training deep neural networks, variational Bayesian inference, and etc. Despite its empirical…
We describe a new approach for managing aleatoric uncertainty in the Reinforcement Learning (RL) paradigm. Instead of selecting actions according to a single statistic, we propose a distributional method based on the second-order stochastic…
The two dimensional BTW model of SOC, with probabilistically nonuniform distribution of particles among the nearest neighbouring sites, is studied by computer simulation. When the value of height variable of a particular site reaches the…
We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty…
In this paper we propose a novel distributed model predictive control (DMPC) based algorithm with a trajectory predictor for a scenario of landing of unmanned aerial vehicles (UAVs) on a moving unmanned surface vehicle (USV). The algorithm…
This paper aims to efficiently compute transport maps between probability distributions arising from particle representation of bio-physical problems. We develop a bidirectional DeepParticle (BDP) method to learn and generate solutions…
Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…
Stein variational gradient descent (SVGD) is a prominent particle-based variational inference method used for sampling a target distribution. SVGD has attracted interest for application in machine-learning techniques such as Bayesian…
This paper develops a unified framework, based on iterated random operator theory, to analyze the convergence of constant stepsize recursive stochastic algorithms (RSAs). RSAs use randomization to efficiently compute expectations, and so…
Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…
A highly adaptive load balancing algorithm for parallel simulations using particle methods, such as molecular dynamics and smoothed particle hydrodynamics (SPH), is developed. Our algorithm is based on the dynamic spatial decomposition of…
In this paper, we study the statistical limits in terms of Sobolev norms of gradient descent for solving inverse problem from randomly sampled noisy observations using a general class of objective functions. Our class of objective functions…
Inferring cellular trajectories from destructive snapshots is complicated by the challenges of stochasticity and non-conservative mass dynamics such as cell proliferation and apoptosis. Existing unbalanced Optimal Transport (OT) methods…
We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective…
In this paper we consider convergence rate problems for stochastic strongly-convex optimization in the non-Euclidean sense with a constraint set over a time-varying multi-agent network. We propose two efficient non-Euclidean stochastic…
Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approximates the gradient as opposed to using the full Jacobian…